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The finite element method is widely used in dental research. The decision to use two-dimensional (2D) or three-dimensional (3D) modelling is dependent on many interrelated factors. The purpose of the present study was to compare and contrast 2D and 3D finite element analysis (FEA) in investigating the mechanical behaviour of a maxillary premolar restored with a full crown under similar conditions of axial and lateral occlusal loading. The 2D analysis required modelling both a buccolingual and mesiodistal section of the restored premolar and for comparison sections of a 3D model were examined. Differences in the results for displacement and maximum principal stress distribution within the component structures and interfaces of the 2D and 3D models were, in general, attributable to differences in geometry represented in the models. Maximum principal stresses tended to be greater under lateral rather than axial occlusal loading. It was concluded that 2D FEA may find application in investigating key aspects of the mechanical behaviour of a dental restoration in a single tooth unit, but that in certain situations combinations of 2D and 3D FEA may offer the best understanding of the biomechanical behaviour of complex dental structures. Sophisticated FE models are required to better understand the mechanical behaviour of restored tooth units.

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The purpose of this study was to investigate, by means of the finite element method the mechanical behaviour of three designs of fixed partial denture (FPD) for the replacement of the maxillary first premolar in shortened dental arch therapy. Two-dimensional, linear, static finite element analyses were carried out to investigate the biomechanics of the FPDs and their supporting structures under different scenarios of occlusal loading. Displacement and stress distribution for each design of FPD were examined, with particular attention being paid to the stress variations along the retainer-abutment--and the periodontal ligament-bone interfaces. The results indicated that displacement and maximum principal stresses in the fixed-fixed, three-unit FPD were substantially less than those in the two-unit cantilever FPDs. Of the two cantilever FPDs investigated, the distal cantilever design was found to suffer less displacement and stresses than the mesial cantilever design under similar conditions of loading. The highest values for maximum principal stress in the cantilever FPDs were found within the connector between the pontic and the retainer, and within the periodontal ligament and adjacent bone on the aspect of the retainer away from the pontic.

Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh—Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.

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